INSURGENT LEARNING * Francesco Trebbi † , Eric Weese ‡ , Austin L. Wright § , and Andrew Shaver ¶ May 25, 2017 Abstract We study a model of insurgent learning during a counterinsurgency campaign. We test empirical implications of the model using newly declassified microdata documenting improvised explosive devices (IEDs) in Afghanistan from 2006 to 2014. This period was characterized by substantial US investments in anti-IED technology and equip- ment. We find no evidence of decreasing effectiveness of IEDs across time. Qualitative evidence suggests that this is due to innovations in IED devices and tactics. Our results are robust to numerous alternative specifications, and yield insights on a technolog- ical revolution in insurgent violence—the proliferation and evolution of IEDs—with implications for scholarship on civil conflict and future investment in tactical counter- measures. * We thank Matilde Bombardini, Ethan Bueno de Mesquita, Hanna Halaburda, Jason Lyall, Thorsten Rogall, Oliver Vanden Eynde, and participants at the Defense and Security Economics Workshop for helpful comments. Members of the Asymmetric Warfare Group provided essential feedback. We also thank the Pearson Institute for the Study and Resolu- tion of Global Conflicts for financial support and various government agencies for providing data. Eli Berman, Kyle Pizzey, and Jacob Shapiro are owed a particular debt of gratitude for their support of this and related projects. All errors remain our own. † Corresponding author: University of British Columbia, Vancouver School of Economics, CIFAR and NBER, [email protected]‡ Kobe University, [email protected]§ University of Chicago, The Pearson Institute, [email protected]¶ Princeton University, [email protected]
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INSURGENT LEARNING∗
Francesco Trebbi†, Eric Weese‡, Austin L. Wright§, and Andrew Shaver¶
May 25, 2017
Abstract
We study a model of insurgent learning during a counterinsurgency campaign. We testempirical implications of the model using newly declassified microdata documentingimprovised explosive devices (IEDs) in Afghanistan from 2006 to 2014. This periodwas characterized by substantial US investments in anti-IED technology and equip-ment. We find no evidence of decreasing effectiveness of IEDs across time. Qualitativeevidence suggests that this is due to innovations in IED devices and tactics. Our resultsare robust to numerous alternative specifications, and yield insights on a technolog-ical revolution in insurgent violence—the proliferation and evolution of IEDs—withimplications for scholarship on civil conflict and future investment in tactical counter-measures.
∗We thank Matilde Bombardini, Ethan Bueno de Mesquita, Hanna Halaburda, JasonLyall, Thorsten Rogall, Oliver Vanden Eynde, and participants at the Defense and SecurityEconomics Workshop for helpful comments. Members of the Asymmetric Warfare Groupprovided essential feedback. We also thank the Pearson Institute for the Study and Resolu-tion of Global Conflicts for financial support and various government agencies for providingdata. Eli Berman, Kyle Pizzey, and Jacob Shapiro are owed a particular debt of gratitudefor their support of this and related projects. All errors remain our own.†Corresponding author: University of British Columbia, Vancouver School of Economics,
Counterinsurgency campaigns are difficult to manage and harder to win. Recent research in
political science and economics investigates a number of difficulties security forces face during
conflicts with insurgent actors. Rebel tactics vary over time [Kalyvas and Balcells 2010;
Wright 2016], development and military aid spending have uneven effects [Berman, Shapiro,
and Felter 2011; Crost, Felter, and Johnston 2014; Beath, Christia, and Enikolopov 2016;
Sexton 2016], their organization is unknown [Dorronsoro 2009; Trebbi and Weese 2015], and
conventional military strategies, including aerial bombardment, can erode civilian support
for the counterinsurgency [Kalyvas 2011; Lyall 2014]. Although states have historically
used mass killings of non-combatants to undermine logistical support for guerrilla actors
[Valentino, Huth, and Balch-Lindsay 2004], evidence from modern insurgencies indicate these
blunt measures may enable mobilization. Rebels may even provoke such indiscriminate state
violence to radicalize the fence-sitting population [Galula 1965; Carter 2016].
In this article, we focus on another major but understudied challenge counterinsurgents
face: insurgent learning. Because it is difficult for counterinsurgents to cloak their warfighting
technologies, insurgents can learn about and exploit weaknesses within deployed forces. Since
counterinsurgents also directly observe insurgent innovations in the field, there are numerous
opportunities for additional investment in defeat techniques.
Although insurgents can learn along many dimensions, we emphasize technological inno-
vation with respect to explosive devices. Explosive devices, especially improvised bombs, are
a frustratingly common and inexpensive tool used by rebel actors. We provide historical ev-
idence of nuanced learning by insurgents regarding bomb making and emplacing techniques.
We then model these conflict dynamics as an investment-based learning game over multiple
periods. Insurgent and government actors independently invest in changes to the technology
they deploy against one another. Reasonably, these investments are observed, and adjust-
ments are made in subsequent periods. Variation in contest success (whether or not a bomb
detonates) is a straightforward empirical metric for evaluating adaptation by each side over
1
time.
We examine insurgent learning using newly declassified microdata on improvised explo-
sive devices (IEDs) during the ongoing Afghanistan conflict. These data allow us to track
the effectiveness of insurgents and counterinsurgents over time. We have information about
latent IEDs cleared before they could be deployed, IEDs that have been planted but were
neutralized by counterinsurgents, and IEDs that were successfully detonated by insurgents.
We use this information to examine changes in the detonation rate over time, during a period
of steadily escalating counterinsurgent investment in IED defeat technologies [U.S. Congress
Oversight Subcommittee 2008]. Consistent with our model, we find little evidence of any
substantial changes in the detonation rate. IEDs were just as likely to explode in 2014 as
they were in 2006.
Our microdata also includes information on the outcomes of IED detonations, including
whether or not the IED event caused any injuries or deaths or vehicle immobilization. We also
know the actors who suffered from bomb damage. Our evidence indicates that, conditional
on detonation, IEDs at the end of the coalition occupation were just as damaging as at the
beginning. We find no evidence of net changes in casualty rates for coalition forces. On the
other hand, Afghan forces who currently carry out nearly all domestic security operations,
experienced a marginally increasing casualty rate over the course of the counterinsurgent
campaign.
These results indicate insurgent learning kept pace with changes in the technological
investments made by counterinsurgents. This fact is sobering given that the United States
alone invested roughly 4 billion dollars a year during the study period on anti-IED research
and development. Starting in 2007, an additional 50 billion dollars was allocated to producing
and deploying IED-resistant vehicles in Iraq and Afghanistan [Wilson 2008]. The Joint IED
Defeat Organization (JIEDDO, now JIDA) spent 2.3 billion dollars to develop and field an
electronic signal jamming device that would thwart IED triggers using two-way radios and
garage door openers [JIEDDO Report 2007]. In response, insurgents simply switched the
2
trigger device. Yet our model suggests these investments were not necessarily wasteful. In
the absence of continued investment in IED defeat operations, the detonation and casualty
rates of insurgent devices would have likely increased.
Our investigation yields insights on a technological revolution in insurgent violence: the
rise and evolution of IEDs. Although rebels (and their state rivals) have weaponized explo-
sive devices for centuries, the recent proliferation of online IED blueprints and substantial
reduction in input costs for bomb production have lead to an unprecedented expansion in
the use of IEDs as a technology of war. IEDs have been reported in a variety of settings in-
cluding Afghanistan, Colombia, India, Iraq, Pakistan, Syria, Thailand, and, in more limited
cases, Mexico, United Kingdom, and United States. With costs ranging from five to several
hundred U.S. dollars, poorly trained and underfunded insurgent organizations can cripple
even the most sophisticated military forces. As a weapon of war, IEDs are now as ubiquitous
as land mines and AK-47s.1 Yet previous research on this technological revolution, and the
learning dynamics that shape the evolving threat posed by IEDs, has been limited by the
restricted nature of microdata on individual IED events.
Our data allows us to explore this technology of war in novel ways. Using newly declas-
sified military records, we are able to examine the location, timing, targets, and outcomes
associated with 94,679 IED-related events from 2006 to 2014. This includes 36,681 IED det-
onations, 43,420 IED neutralizations, and 14,578 weapon cache discoveries. We are able to
examine national and regional trends in IED effectiveness over the course of the campaign,
as well as decompose changes in the rate of learning by insurgents specific to different types
of actors over time.
1The recent use of IEDs by terrorists also highlights the changing nature of destructivetechnologies available to weak yet violent political actors. Attacks on London’s public trans-portation system, Boston’s 2013 marathon, and the May 2017 Manchester Arena attack wereall conducted using IEDs and resulted collectively in nearly one hundred civilian deaths andsome one thousand injuries. Some of the perpetrators of these attacks—for instance, theTsarnaev brothers, responsible for the Boston attacks—had no military background or spe-cialized educational training necessary otherwise required for the production of sophisticatedexplosive devices.
3
This paper also brings together the rich literature in political science and economics on
learning by strategic actors with recent work on counterinsurgency. Research on learning
highlights how policies diffuse across governments [Mebane and Sekhon 2002; Volden, Ting,
and Carpenter 2008; Callander 2011; Makse and Volden 2011; Callander and Clark 2017],
communication devices enable anti-regime protests to spread [Little 2015], ethnic kin learn
from government repression [Larson and Lewis 2017], unit leaders learn during deployments
[Bueno de Mesquita, Price, and Shaver 2017], and firms and individuals innovate in response
to productivity shocks [Bahk and Gort 1993; Young 1993; Foster and Rosenzweig 1995;
Conley and Udry 2010]. These papers highlight how actors adapt their behavior in a dynamic
fashion. Our model similarly highlights the importance of continuous feedback in strategic
settings, from voting and firm production to insurgent innovation. Our model of insurgent
learning also yields a number of important insights about the features of a counterinsurgency
campaign that we believe are not fully captured in existing models of strategic interaction
between warring actors such as those of Bueno de Mesquita and Dickson [2007], Fey and
Ramsay [2007], and Bueno de Mesquita [2016].
The rest of the paper is organized as follows. In the next section, we briefly outline
historical evidence of learning by rebel actors. In Section 3, we present a model of sequential
learning in a dynamic environment. In Section 4, we present an overview of our data and
empirical strategy. Section 5 presents visual and regression-based evidence of insurgent
learning. The final section concludes.
2 Insurgent Learning
Insurgencies are typically characterized by substantial asymmetries in capabilities. Armed
groups must recruit, train, and arm fighters, gather intelligence on government targets and
their vulnerabilities, and establish funding streams, all in the presence of more capable
government forces. These government forces vary their investments in counterinsurgent
4
technologies and institutions, including measures taken to harden stationary targets and to
randomly adjust movements of mobile targets [Hayden 2013]. Rebels respond to government
countermeasures through adaptation. Adaptation, on both sides, is dynamic [Jackson 2004].
Existing research provides ample qualitative evidence of learning across insurgencies [For-
est 2009].2 The Irish Republican Army (IRA), for example, transferred detailed information
about bomb making and mortar design to armed groups in Colombia, Palestine, and Spain.
Before the US-led invasion, the Afghan Taliban operated a number of training camps at-
tended by various Pakistani rebel factions as well as fighters affiliated with al Qaida. Even in
the absence of formal coordination, groups learn from one another. Al Qaida modeled their
2001 bombing of the USS Cole on a similar, highly publicized 1995 operation carried out
by the Tamil Tigers. Insurgents in the Deep South region of Thailand have modeled their
recent explosive devices on designs developed by sectarian fighters in Iraq [Abuza 2007].
The qualitative record on innovations within insurgencies is equally rich [Jackson et al.
2005]. To enhance the precision timing of their attacks, the Irish Republican Army adapted
the Memopark timer for use in munition detonation. The Memopark timer was a simple,
handheld device used for tracking remaining meter time on parked vehicles. Because this
device was widely available and difficult for counterinsurgent forces to track, the IRA did not
develop new timer technologies for years after the first Memopark explosive. Thai insurgents
have also adapted how to design and plant roadside bombs to avoid detection, including
sophisticated techniques for hiding bombs in objects commonly discarded along the main
traffic corridor from Yala to Pattani.
In Iraq and Afghanistan, IED technology has rapidly advanced, from primitive wire-to-
battery devices to bombs detonated through encrypted radio signals. Importantly, these
innovations typically occur in response to countermeasures taken by security forces. For
example, a simple pressure-plate IED detonates when a vehicle rolls over it, thereby depress-
ing the plate. A counter-measure for this type of IED is a roller in front of the vehicle: the
2Revolutionaries and counterrevolutionaries also learn from one another [Weyland 2016].
5
IED will detonate when the roller passes over it, potentially destroying the (relatively cheap)
roller, but leaving the vehicle and its occupants unharmed. A counter-counter-measure, how-
ever, is to separate the pressure plate from the explosive, so that when the roller rolls over
the pressure plate and detonates the explosive, the vehicle behind the roller is located above
the explosive. This sequence of adaptation was observed between 2006 and 2007 [JIEDDO
Report 2007].
We focus on learning within insurgencies, with a special emphasis on explosive devices.
Rebel groups carry out bombings with a certain technology composite. This technology sig-
nature includes emplacement location, bomb size, explosive force, and detonation technology.
Observing this bombing composite, government forces respond by introducing countermea-
sures. These countermeasures include randomizing force movement, enhancing vehicle and
body armor, and developing signal jammers. Taking into account the government’s re-
sponse, rebels adapt their bombing technologies. Before rebels adapt to the government’s
countermeasures, these security innovations should decrease the effectiveness of IEDs de-
ployed against security forces. After rebels adapt to these countermeasures, the effectiveness
of IEDs should increase. We formalize this logic below.
3 A Model of Learning
We focus on an conflict environment with one insurgency force A and a government-aligned
counterinsurgency force G. We assume time is discrete and the conflict is expected to last
T periods t = 1, ..., T .3 Let us indicate with r the discount rate and with Y A and Y G the
respective exogenous total endowments of the two actors. For realism, one can consider it
to be the case that 0 < Y A � Y G.
In each period t, A can make an investment 0 ≤ IAt ≤ Y A in attacking capability to
augment its current stock ACt−1. In each period t, G also makes a nonnegative investment
3For the case of Afghanistan, this could be equivalent to a planned and publicly announcedwithdrawal of troops.
6
0 ≤ IGt ≤ Y G in defensive technology to augment its current stock DFt−1.
We allow both A and G to learn over time from previous conflict experience. It seems
intuitive to assume that some form of learning may occur by repeated interaction, so that,
for example, the past stock of defensive technology DFt−1 may offer opportunity of learning
to A by augmenting its attacking capability ACt. Specifically we posit for A the simple
dynamic process:
ACt = αACt−1 + γDFt−1 + IAt
and similarly for G:
DFt = αDFt−1 + ρACt−1 + IGt .
The processes described above include a realistic component of autocorrelation in conflict
capability, indexed by 0 ≤ α ≤ 1. In addition, learning implies that a defensive investment
on the part of counterinsurgency forces at period t, IGt , can feedback in higher offensive
capability by the insurgents in period t + 1 by a factor 0 ≤ γ ≤ 1 per unit of investment.
Symmetrically, learning operates with a factor 0 ≤ ρ ≤ 1 for the counterinsurgency forces.
We assume that in every period t there is a conflict event resolved through a conflict
function of the Tullock [1980] form. It posits the probability of a victory for the insurgents
equal to:
Pr(A’s success at t) =ACt
ACt +DFt. (1)
We can think of equation (1) as a metric of “effectiveness” in conflict for the insurgent force,
for which IED effectiveness (i.e. detonation rate and casualty rate) may be considered a
valid empirical proxy in our context.
Finally, let us assume the cost of investment is linear at a per unit cost c ≥ 0 for both A
and G (symmetry is an assumption trivially relaxable here).
The insurgency force A will have valuation:
V A =T∑t=1
[ACt
ACt +DFt− cIAt
](1 + r)−(t−1) ,
7
which A will maximize with respect to the intertemporal investment profile{IAt}Tt=1
subject
to the budget constraintT∑t=1
IAt (1 + r)−(t−1) ≤ Y A
and optimal response by G.4
In this simple theoretical environment it is possible to observe that the effectiveness in
conflict of the insurgents vis-a-vis counterinsurgency forces will change over time. It is based
on the countervailing effects arising from the fact that investing in offensive technology today
increases the probability of success today and, with an α depreciation, tomorrow, but also
increases the conflict capability of its adversary tomorrow by a factor of ρ.
To gain insight on the dynamic effects due to learning it is sufficient to set T = 2 and
study the evolution over time of the object (1). To make our results less cumbersome, we
set AC0 = DF0 = 0.
We can then prove the following proposition.
Proposition 1. Consider the two period model. Then there exists a unique Nash Equilibrium
of this game. Further, (i) the effectiveness of A is constant between period 1 and 2 only if the
learning process is proportional to resources, i.e. if ρ/γ =(Y G/Y A
)2. (ii) The effectiveness
of the insurgents, ACt
ACt+DFt, increases (decreases) over time if the learning process favors the
counterinsurgency (insurgency) forces, i.e. if ρ/γ >(Y G/Y A
)2(if ρ/γ <
(Y G/Y A
)2).
Proof. In Appendix.
4Similarly for G we study:
max{IGt }Tt=1
T∑t=1
[DFt
ACt +DFt− cIGt
](1 + r)−(t−1)
subject toT∑t=1
IGt (1 + r)−(t−1) ≤ Y G.
8
The proposition posits first an intuitive result. Suppose counterfactually that Y A = Y G, then
the effectiveness of the insurgent forces remains constant over time if the learning processes of
A and G move at the same rate, i.e. the learning is symmetric (ρ = γ). Since however initial
resources are skewed in favor of G and a large initial investment by G favors A’s learning,
the insurgency will be able to keep a constant effectiveness rate even with an asymmetry in
learning ratio ρ/γ if ρ/γ matches the endowment imbalance(Y G/Y A
)2.
The proposition also highlights another result. The effectiveness of the insurgents will
increase over time as T nears, if they operate at a learning disadvantage relative to the
counterinsurgency forces (ρ > γ(Y G/Y A
)2).5 The intuition is that, as A learns substantially
more slowly than G in this case, then A has an incentive to initially underinvest in offensive
technology in order not to excessively prop up G’s success probabilities in the following
periods. At the same time, because its adversary does not learn as much, G has an incentive
to over-invest in defensive capacity relative to a hypothetical case without such learning
effects. Hence, in this case it follows that AC1
AC1+DF1< AC2
AC2+DF2(increasing effectiveness of A).
We can also prove the following result.
Proposition 2. Consider the equilibrium of two period model. If the effectiveness of the
insurgents, ACt
ACt+DFt, increases over time, i.e. ρ/γ >
(Y G/Y A
)2, then the growth rate of
investment for insurgents is larger than the growth rate of investment for counterinsurgents,
i.e.IA2IA1
>IG2IG1
. Similarly, if the effectiveness of the insurgents decreases over time, (ρ/γ <(Y G/Y A
)2), then the growth rate of investment for insurgents is smaller than the growth
rate of investment for counterinsurgents, i.e.IA2IA1<
IG2IG1
.
Proof. In Appendix.
This proposition focuses on an important dynamic. If the effectiveness of insurgents is in-
creasing from one period to the next, the relative change of insurgent investment in techno-
logical innovation must exceed the change in government investments. Relatedly, any decline
5The reader will note here that the restriction ρ ≥ γ seems the empirically realistic onefor the Afghan case.
9
in bomb success over periods is a function of government investments outstripping insurgent
inputs in relative terms. Notice that this result also obtains if one or the other actor divests
over time at a faster rate than their opponent. That is to say, if counterinsurgent forces
draw down their investments between periods, while insurgent investments remain constant
(or increase) between periods, attack effectiveness will increase. The inverse obtains as well.
4 Data and Empirical Strategy
Our investigation exploits newly declassified conflict data from the United States Central
Command. The data was retrieved by [Author] and [Author]. The detailed nature of this
conflict data allows us to track insurgent activity by the hour, to within several meters of the
event location. Although this data tracks dozens of types of violence, the majority of enemy
action events are characterized as direct fire, indirect fire, and IED explosions. Direct fire
consists of machine guns, AK-47s, and other weapons that are effectively fired on a straight
line from attacker to target. Indirect fire consists of mortars and other weapons that do not
depend on a line of sight between the attacker and the target. IEDs consist of explosives that
have already been emplaced, and are simply detonated by the attacker at the appropriate
time.
This paper focuses on insurgent learning with respect to IEDs. For each event, we
know the exact location (within several meters), time (within the hour), and detonation
status (whether the IED exploded or was neutralized). Importantly, emplaced IEDs are
not typically retrieved from the field and replanted elsewhere. For IEDs that detonate, we
also know the institutional affiliation the target (Coalition, Host Nation), the type of actor
(Military, Police), and the outcome of the event (Ineffective, Damaged/Disabled/Destroyed,
Injured, Killed).
The last three of these categories form an ordered scale, describing the effect of the
insurgent attack on Afghan/Coalition forces: if an Afghan or Coalition security force member
10
Figure 1: IED events: detonate/clear and explosion impacts
Figure SI-4 shows the numbers of IED attacks targetting coalition forces, supported
Afghan troops, and unsupported Afghan troops, respectively. For IED explosions targetting
coalition troops, there appears to be no change in casualty rates. For Afghan government
forces, casualty rates appear to be increasing in recent years.7
Within the Afghan military, however, certain units are supported by coalition forces.
Coalition advisors in these units not only provide advice, but also bring with them sophis-
ticated technology. We thus might expect that Afghan military units that are supported by
coalition troops perform differently than those that are not. Figures SI-4e and SI-4f show
that this is indeed the case. The casualty rate for Afghan military units with coalition sup-
port is close to 50%, while the rate for unsupported units is closer to 75%. There is no clear
trend visible in Figures SI-4e or SI-4f.
The sharp increase in casualty rates shown in Figures SI-2 and SI-3 thus appears to be
due to a compositional trend in the target of IED attacks. From 2010 onwards, the number
7We provide a regression analysis of this claim in Tables A-5 and A-6.
18
of coalition troops targetted by IEDs declined. These coalition troops were first replaced by
Afghan troops supported by coalition forces, and then later by unsupported Afghan troops.
As these types of troops are more vulnerable to IED attacks, we see an increase in the overall
casualty rate. Within a given type of unit, there is little to no change in casualty rates. We
present a statistical analysis of these results below. This analysis shows that if anything
there are small increases in the casualty rate (conditional on IED explosion) across time.8
The fact that casualty rates for coalition forces do not change or even increase slightly is a
surprising result. Armoured vehicles were becoming increasingly prevalent during this period,
and there were a wide variety of new anti-IED technologies being deployed by JIEDDO.
The lack of a trend in Figure SI-4a, then, is evidence that either this new equipment and
technology was actually useless, or that there was also substantial improvement in the quality
of IEDs during this period.
5.2 Regression-based evidence
We are interested in testing whether the visual evidence reviewed above is statistically robust.
We begin with Figure 2. We examine whether Figure 2 has no substantial trend in
clearance rate (fraction of IEDs that are found before they explode) or if this trend is
significantly increasing or decreasing over time.
We consider our unit of observation to be the individual IED. This IED could be emplaced
and explode, or it could be emplaced but then found and cleared, or it could be found and
cleared before it was emplaced (“cache found and cleared”). We will use a binary variable
“did IED explode?” as our outcome variable Y , coded as 0 if the IED was found and cleared.9
8The sole exception is for coalition supported Afghan military units.9Some IEDs are missing from the dataset: those that explode when nobody is around to
notice, those that explode on civilian targets but happen to not be reported to the authorities,those that have neither exploded nor been found and cleared yet. Our analysis assumes thatthe nature of this missing data does not change across time. In general we would expectthe reporting process to improve over time, and thus the clearance rate should drop. Ourfinding that it is does not drop is thus more surprising given the sign of the expected bias.
19
A linear probability model will be used with the form
Pr(Yigm = exploded) = βTimeigm + αg + γm.
Here the probability of observing a given outcome (exploded vs. found and cleared) for
IED i in lat-lon grid square g in month of year m is determined by the continuous variable
Time (coded as 0 for midnight on 1 January 2006 and around 8.83 at the end of our sample
period in November 2014).
Results from this regression are shown in Table A-1. Importantly, positive coefficients
indicate that the detonation rate is increasing (and, conversely, that the clearance rate is
decreasing). Columns 1-4 show that there is no statistically significant trend in IED clearance
rates over time, and that this result is the same regardless of whether grid square and month
of year fixed effects are included. This result is also unchanged when only emplaced IEDs
are considered (that is, “cache found and cleared” observations are dropped).10
Alternatively, if we instead employ a logit model specification and replicate Table A-1,
we find consistent evidence that the rate at which IEDs detonate is increasing throughout
the conflict. These results are displayed in Table A-2. In principle, this functional form
might be a better fit for our dichotomous outcome variable. Importantly, this increasing
detonation rate is robust across columns 1-4, which vary grid square and month of year fixed
effects. Although there is disagreement between Tables A-1 and A-2 over the statistical
significance of the time trend, we can squarely reject a significant increase in clearance rates
at the country level.11 That is, counterinsurgents were no better at clearing explosive threats
from the field in 2014 than they were in 2006.
There is no reason to believe that there is differential reporting issues in Panjwai.10Columns 2 and 4 do not have an intercept term because it is absorbed in the fixed effects.11Using the coefficient reported in column 1 of Table A-2, we see that from 2006 to 2014
the log odds ratio for an IED exploding increased by 0.016× 8 = 0.128. This means that ifthe odds of an IED exploding in 2006 were 37%, they rose to 40% in 2014. This is oppositeto the naive prediction that spending on IED defeat technologies should have reduced therate at which IEDs exploded.
20
We now consider what happens conditional on an IED exploding. The potential outcomes
in this case are “Ineffective”, “Dam/Dis/Destroyed”, “Wounded”, and “Killed”.12 We thus
have four discrete ordered outcomes: “Ineffective” < “Dam/Dis/Destroyed” < “Wounded”
< “Killed”. One option is to analyze this as is, using an ordered logit framework. Another
option is to collapse the outcome variable to a binary variable, and analyze using the same
sort of standard linear probability model used above.
First, consider the ordered logit case. Here the observed discrete outcome Y is determined
by a latent continuous variable Y ∗, and an additional parameter vector µ is estimated that
gives cutoff values that provide the mapping of the continuous variable Y ∗ into the discrete
variable Y . We suppose that the process determining Y ∗ is
Y ∗igm = β1Timeigm + β2TYPEigm + β3(Time x TYPE)igm + αg + γm + εigm
Here Time is the same continuous variable as was used above. TYPE is the type of
the unit encountering the IED: the options here are “Afghan Military, Supported”, “Afghan
Military, Unsupported”, “Afghan Police”, “Civilian”, “Coalition”, and “NA”, where a large
portion of the “NA” explosions were IEDs that were targetting an inanimate object, such
as a bridge or important building. The length of β2 and β3 would thus both be six, but a
normalization implied in the estimation of the cutoffs µ means that only five parameters in
β2 will actually be estimated.
Table A-3 shows the results of this approach. We see that overall IEDs are more deadly
when employed against soft targets such as civilians, and less deadly when employed against
Coalition forces.13 The time trends estimated in Column 3 show that there is no statistically
12Some outcomes are marked as “NA”. Qualitative evidence leads us to conclude that ex-plosions classified as “NA” did not cause damage, and thus we group “NA” and “Ineffective”together and label this group as “Ineffective”.
13The base level here is “Afghan Military, Supported”, which makes the positive coefficienton “Afghan Military, Unsupported” in Column 3 surprising, since one would expect thatsupported troops would be a harder target than unsupported troops. This effect disappears,
21
significant relationship for coalition outcomes over time. The (statistically insignificant)
estimated parameter of 0.015 for “Time x Coalition” implies that from 2006 to 2014, the log
odds ratio for coalition forces suffering a casualty (versus no casualties) increased by only
0.015 × 8 = 0.12. This means that if coalition forces suffered casualties 30% of the time in
2006, they would suffer casualties 32.5% of the time in 2014. The estimated trend over time
is thus not only statistically insignificant but also small, as well as being in the opposite
direction from what would be expected given the large investments made in armour and
various other IED countermeasures.14
A potential concern at this point is that the ordered logit model considered above may rely
on assumptions that are violated in the data. For example, perhaps idiosyncratic shocks are
not distributed according to an extreme value distribution. To assess the robustness of our
results, we convert our ordered discrete outcome to a binary outcome: we classify explosions
that are “Ineffective” or result in “Dam/Dis/Destroyed” as not causing a casualty, and
explosions that result in “Wounded” or “Killed” as explosions that do cause a casualty. We
then consider a linear probability model of the form,
The results of this regression are shown in Table A-4. Results are generally very similar:
some of the time trends interactions reported in Table A-3 are not statistically significant in
Table A-4, although the coefficient estimates are in the same direction.15
however, in Column 4, and instead we see a time trend that makes supported Afghan troopsless likely to become casualties in later periods. One potential explanation is that initiallysupported Afghan troops are deployed to particularly dangerous areas, and the averagedanger of these areas decreases as the number of supported troops increases over time.
14The very large time trend in “NA” type targets is probably due to a compositional trendwithin these targets: if some targets in the early period did not have any people near them,then casualties could not be recorded. This could result in large increases in the casualtyrate as time progressed.
15The particular implementation of wild bootstrap clustered standard errors used to report
22
A final issue relates to Figure 3b. Careful inspection of this figure suggests that there
may be time trends in casualty rates for IEDs that potentially differ from grid square to grid
square. These effects appear to be due to compositional changes in targets across time. To
show this, we consider a regression following Table A-4. In particular, when we condition on
the type of target (Coalition, Civilian, Afghan Police, Afghan Military Supported, Afghan
Military Unsupported) we find that estimated time trends at the district level are nearly
indistinguishable from random noise based on an F test (p ' .1). For direct fire attacks, the
distribution of casualties (Figure SI-8b) is less even across districts than for IED attacks.
This could indicate greater planning in the very small number of attacks that are carried
out in the north, or under-reporting of unsuccessful attacks in that region.
We conclude our examination with a within-week analysis of detonation and casualty
rates by district during the Afghan campaign. We continue to code these measures as
described above. We begin with detonation rates and then decompose harm from IEDs
that detonate into Coalition and Afghan casualty rates. These outcomes are only defined
for district-weeks with at least one explosives attack. These rate outcomes are continuous,
but bounded by zero and one. We begin with an ordinary least squares specification and
confirm robustness to a generalized least squares model with binomial family and logit link
functions. This latter specification is commonly used for rate outcomes. We estimate the
following equation,
Ydw = β1Timedw + αw + γd + εdw,
Where Ydw denotes the three outcomes of interest (detonation, Coalition casualty, and
Afghan casualty rates) and is defined for each district-week with positive levels of IED
activity. Week of year and district fixed effects are included in all models, with even numbered
results in Table A-4 gives coefficient estimates for the Time x TYPE coefficients in termsof differences from the base level of “Time x Afghan Military, Supported”. The coefficentestimate for this level is close to zero (as reported in the “Time” row), and thus interpretationis mostly unaffected by this difference.
23
columns including a year fixed effect. The coefficient of interest is β1. If β1 is positive, this
indicates that the detonation rate or casualty rates are increasing during the campaign.
These results are shown in tables A-5 and A-6. Recall, the even numbered columns
in each table introduce year fixed effects. With respect to detonation rates, these results
indicate that the likelihood of explosion is either flat or significantly increasing during the
campaign. Importantly, these results obtain even when conditioning out district-specific but
and, through the budget constraints (2), we also have the unique equilibrium IA2 and IG2 .
This construction proves existence and uniqueness of the Nash equilibrium.
Consider now the equilibrium insurgent effectiveness at periods 1 and 2 obtained by using
the players’ equilibrium investment strategies:
AC1
AC1 +DF1
=χY A + γY G
(χ+ ρ)Y A + (χ+ γ)Y G
AC2
AC2 +DF2
=Y A
Y A + Y G.
A-2
Notice then that
χY A + γY G
(χ+ ρ)Y A + (χ+ γ)Y G=
Y A
Y A + Y G
if it holds that
γ(Y G)2 − ρ (Y A
)2(Y A + Y G) ((χ+ ρ)Y A + (χ+ γ)Y G)
= 0
or
ρ
γ=
(Y G
Y A
)2
.
Notice further that
AC1
AC1 +DF1
<AC2
AC2 +DF2
⇒(Y G
Y A
)2
<ρ
γ.
This proves the proposition. �
A-3
Proof of Proposition 2. Consider that
ρ/γ >(Y G/Y A
)2implies
ρ(Y A)2 − γ (Y G
)2χY A + γY G
> 0
and notice that
ρ(Y A)2 − γ (Y G
)2χY A + γY G
=IG1IA1− Y G
Y A.
So from the argument above it holds that
IG1IA1− Y G
Y A> 0,
then this implies that the difference
IG2IG1− IA2IA1
=
(Y GIA1 − Y AIG1
) (1 + r)
Y AY G< 0.
This proves the proposition. �
A-4
B Main results and summary statistics
Table A-1: Trends in IED explosions (binary outcome)
(1) (2) (3) (4) (5) (6)All All All All Panjwai Panjwai
Time 0.004 0.002 0.004 0.002 −0.032∗∗∗ −0.031∗∗∗
(0.007) (0.005) (0.004) (0.002) (0.004) (0.004)Grid square FE No Yes No Yes No NoMonth of year FE No Yes No Yes No YesN 94,679 94,679 80,101 80,101 6,673 6,673R2 0.0002 0.407 0.0002 0.469 0.011 0.408Adjusted R2 0.0002 0.406 0.0002 0.469 0.011 0.407
∗p < .1; ∗∗p < .05; ∗∗∗p < .01
Columns 1 and 2 consider only emplaced IEDs (coded 0 if the IED was then found andcleared, and 1 if it exploded). Columns 3 and 4 also include caches that are found andcleared (these are coded as zeros). Columns 5 and 6 are restricted to the Panjwai region.Grid square fixed effects (FE) are not used because Panjwai is entirely contained in the 66E32N grid square. Columns 1-4 use errors clustered at the grid square level. Columns 5-6 useheteroskedasticity consistent covariance matrix estimates.
Table A-2: Trends in IED explosions (binary outcome), using logit model specification
(1) (2) (3) (4) (5) (6)All All All All Panjwai Panjwai
Time 0.016∗∗∗ 0.009∗∗∗ 0.015∗∗∗ 0.008∗∗ −0.134∗∗∗ −0.133∗∗∗
(0.003) (0.004) (0.004) (0.004) (0.015) (0.016)Grid square FE No Yes No Yes No NoMonth of year FE No Yes No Yes No YesN 94,679 94,679 80,101 80,101 6,673 6,673
∗p < .1; ∗∗p < .05; ∗∗∗p < .01
Logit model. Columns 1 and 2 consider only emplaced IEDs (coded 0 if the IED was thenfound and cleared, and 1 if it exploded). Columns 3 and 4 also include caches that are foundand cleared (these are coded as zeros). Columns 5 and 6 are restricted to the Panjwai region.Grid square fixed effects (FE) are not used because Panjwai is entirely contained in the 66E32N grid square.
Standard errors in parenthesesγ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
All models include district and week-of-year fixed effects (FE). Standard errors are clusteredby district. Even numbered columns include a year fixed effect. Time is a linear trend. Themodel is estimated using ordinary least squares.
Standard errors in parenthesesγ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
All models include district and week-of-year fixed effects (FE). Standard errors are clusteredby district. Even numbered columns include a year fixed effect. Time is a linear trend. Themodel is estimated using generalized least squares, with a binomial family and logit linkfunctions.
A-8
Table A-7: Summary Statistics for Tables A-1 and A-2
Each observation has an outcome that is one of “Ineffective”, “Dam/Dis/Destroyed”,“Wounded”, and “Killed”. “Casualty” is coded as 1 when the outcome is either “Wounded”or “Killed”. Each observation has a TYPE that is one of “Afghan Military, Supported”,“Afghan Military, Unsupported”, “Afghan Police”, “Civilian”, “Coalition”, and “NA”.
Table A-9: Summary Statistics for Tables A-5 and A-6
IED Explosion IED Found & Cleared Cache Found & Cleared
D.2 Regression-based evidence
The results below correspond to the estimating equations and functional form specifications
reported in the main text.
In Table A-1, Columns 5 and 6 show that in Panjwai there is a positive time trend in the
clearance rate: that is, the percentage of IEDs that explode is decreasing over time. This
trend is the same when controlling for seasonality by adding month of year fixed effects.
In Table A-3, Columns 5-8 consider only IED explosions in the Panjwai area. Results
in Columns 5-8 are the same as those in Columns 1-3. We see that over time, IEDs have
become deadlier; however, as discussed in the main text, this appears to be mainly due
to a compositional change away from coalition forces and towards more vulnerable Afghan
troops.
Column 8 shows some differences between Panjwai and Afghanistan as a whole. In
particular, the positive trend in coalition casualty rates is larger and statistically significant.17
17Note, however, that this effect is statistically insignificant in the alternate specification
SI-13
That is, we observe increasing casualty rates in an environment that we know qualitatively
resulted in a coalition victory.18 This suggests that casualty rates would be an extremely
poor tool to use to assess whether an insurgency is winning or loosing a conflict. Figure
SI-10 suggests that this is true in other cases as well: historical data on casualty rates from
the Vietnam war does not show rising success rates against US sorties.19
Several explanations are possible here. First, coalition forces might have been more care-
ful in a known battle zone than in an area that is generally regarded as secured. For example,
they may use lighter vehicles or may dismount from their vehicles more frequently. Second,
insurgents launching many IED attacks may have used IEDs at times or locations that are
not optimal, while a much smaller insurgent force could act only on the best opportunities.
Third, the incentives for insurgents may be very different in an area where they have lost
control, when compared to an area where there is a high intensity battle. For example, in a
battle with known front lines, pressure plate IEDs can be emplaced to discourage movement
in certain areas, and this tactic could be effective even when the casualty rate from these
presented in Table A-4.18Quantitatively, this trend is equivalent to an increase in casualty rates from 50% to
67%, which matches fairly well with Figure SI-13. We do not conduct a formal test of theproportionality assumption of the ordered logit regression.
19There is a notable contrast between flat casualty rates in asymmetric warfare such asAfghanistan and Vietnam, and sharply changing kill ratios in air combat in world war II[Mersky 1993]. Some of the change in kill ratios towards the American’s favour was dueto improved fighter technology. Tactical changes that were free to disseminate, however,also resulted in substantial improved performance against the Japanese Mitsubishi Zero.For example, the Thach Weave was extremely low cost to develop, effective in dogfights, andalmost impossible to counter [Ewing 2013]. This sort of development in tactics is reminiscentof insurgent warfare because it originated in an asymmetry: the American wildcat fighterswere noticeably less maneuverable in combat than the Japanese zeros, and thus could nottake them on directly in a one-on-one dogfight.
Another well known example of tactical development in conventional warfare concernsgrenades in urban combat. These are particularly useful for clearing buildings, and thusdefenders sometimes seek protection by covering windows with chicken wire to deflect throwngrenades. The appropriate response, (re-)discovered repeatedly around the world from the19th century onwards, is to attach fishhooks to the grenades. This approach was also usedduring asymmetric warfare in Vietnam [Zahn 2003].
SI-14
IEDs is relatively low. Such a tactic has little value in a much lower intensity conflict when
the government forces are clearly in control of the area.20
20Additionally, damaging or disabling a vehicle may be valuable when fighting a battlein which the absence of that vehicle on the battlefield in the following days could make adifference; in contrast, damaging a vehicle during a very low intensity conflict may be of littleimportance, because the vehicle will be repaired before any subsequent attacks are launched.